3x-1(4x-3)=(3x+3)2x

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Solution for 3x-1(4x-3)=(3x+3)2x equation: 


Simplifying
3x + -1(4x + -3) = (3x + 3) * 2x

Reorder the terms:
3x + -1(-3 + 4x) = (3x + 3) * 2x
3x + (-3 * -1 + 4x * -1) = (3x + 3) * 2x
3x + (3 + -4x) = (3x + 3) * 2x

Reorder the terms:
3 + 3x + -4x = (3x + 3) * 2x

Combine like terms: 3x + -4x = -1x
3 + -1x = (3x + 3) * 2x

Reorder the terms:
3 + -1x = (3 + 3x) * 2x

Reorder the terms for easier multiplication:
3 + -1x = 2x(3 + 3x)
3 + -1x = (3 * 2x + 3x * 2x)
3 + -1x = (6x + 6x2)

Solving
3 + -1x = 6x + 6x2

Solving for variable 'x'.

Combine like terms: -1x + -6x = -7x
3 + -7x + -6x2 = 6x + 6x2 + -6x + -6x2

Reorder the terms:
3 + -7x + -6x2 = 6x + -6x + 6x2 + -6x2

Combine like terms: 6x + -6x = 0
3 + -7x + -6x2 = 0 + 6x2 + -6x2
3 + -7x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
3 + -7x + -6x2 = 0

Factor a trinomial.
(1 + -3x)(3 + 2x) = 0


Subproblem 1
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {0.3333333333, -1.5}

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